Publications and other reference materials referred to herein are numerically referenced in the following text and respectively grouped in the appended Bibliography which immediately precedes the claims.
Fano resonances arise when two transmission pathways, a broad band continuum and a narrow band resonance, interfere with each other [1]. When one of the channels is a highly damped resonance process, its exact resonant frequency is difficult to detect and such a channel can be considered as a broad band continuum. The physical origin of Fano resonances can be understood simply from the dynamics of a system of coupled oscillators. The Fano-resonant phenomenon appears as a notch in the absorption spectrum when the incident electromagnetic wave couples to a strongly damped oscillator, which in turn is coupled to a weakly damped mode. The resulting effective coupling between the two modes is dispersive, i.e., it depends strongly on the frequency in a narrow interval around the frequency of the weakly damped oscillator and gives rise to a strong modulation of the absorption spectrum. Presently, these effects are widely used in optical spectroscopy of biological structures [2, 3]. At the same time, there are no publications, to the best of the inventor's knowledge, on the Fano-resonant spectroscopy of biological structures in microwaves.
Study of microwave properties of biological liquids is one of the most important problems in biophysics. Microwave absorption is primarily a tool for observing and measuring different kinetic processes in biological liquids. It may concern molecule rotational transitions and vibrational resonances in biological systems. Microwave absorption resonances are observed in aqueous solutions of DNA [4-7]. The success of a spectroscopic technique depends on two main problems: one is the availability of accurate data over the required frequency range while the other is the ability to unambiguously interpret this data. These two problems have a special aspect in spectroscopic characterization of high lossy materials. The temporal and spatial resonant nature of an electromagnetic standing wave within a dissipative media is obscure and incoherent. Spatially, regions with maximum magnetic (electric) field and null electric (magnetic) field can no longer be well defined and separated. One of the topical subjects on the lossy-material characterization concerns microwave analyses of biological liquids. Proper correlation of the measured parameters with structural characteristics of chemical and biological objects in microwaves appears as a serious problem. Nowadays, microwave bio-sensing is mainly represented by the microwave-cavity technique and the transmission/reflection technique [8-15]. The microwave-cavity technique is based on the well-known perturbation method used for measuring dielectric properties of materials. The resonant techniques, however, are not suitable for high-lossy liquids because the resonance peak is so broad that the perturbation characteristics cannot be measured correctly. Also, interpretation of the data obtained from the transmission/reflection technique cannot be considered as sufficiently suitable for high-lossy liquids.
In numerous microwave experiments, a problem of the high-lossy-material characterization is formulated in order to obtain data on the permittivity and permeability parameters, which are represented as a combination of real and imaginary parts, i.e. ∈′, ∈″ and μ′, μ″. It appears, however, that such representation of parameters and, moreover, interpretation that these data properly characterize high-lossy materials may be beyond a physical meaning. This statement is clarified by the following consideration. It is known that electromagnetic processes in a non-conductive medium are described, energetically, by Poyning's theorem which, when represented in the form of the continuous equation:
                                                        ∇              →                        ⁢                          ·                              S                →                                              =                                                    ∂                w                                            ∂                t                                      +            q                          ,                            (        1        )            shows that divergence of the power flow density {right arrow over (S)} is determined by two quantities: time variation of the electromagnetic-field density w and density the dissipation losses q. For an isotropic temporally dispersive medium, described by constitutive parameters ∈(ω)=∈′(ω)+i∈″(ω) and μ(ω)=μ′(ω)+iμ′(ω), the two terms in the right-hand side of Eq. (1) have definite physical meaning (and so can be considered separately) only when|∈″(ω)|<<|∈′(ω)| and |μ″(ω)|<<|μ′(ω)|  (2)The frequency regions where |∈″(ω)| and |μ″(ω)| are small compared to |∈′(ω)| are |μ′(ω)| are called the regions of transparency of a medium. Only inside transparency regions can one separately introduce a notion of the electromagnetic-field density w (which is related to the real-part quantities ∈′ and ∈′) and a notion of density the dissipation losses q (which is related to the imaginary-part quantities ∈″ and μ″). The energy balance equation (1) for such a transparent medium is described by quasi-monochromatic fields [16]. For a non-transparent medium (or in a frequency region of medium non-transparency), relations (2) are unrealizable and one cannot describe the right-hand side of Eq. (1) by two separate and physically justified terms. This is the case of a high lossy (or high absorption) medium. In a high lossy medium, one cannot state that the electromagnetic-field density w and density the dissipation losses q are separate notions with definite physical meaning. In such a case, there is no meaning to consider quantities ∈′ and μ′ as physical parameters related to energy accumulation and quantities ∈″ and μ″ as physical parameters related to energy dissipation.
In all the known experiments for characterization of high-lossy material parameters, the quasi-monochromatic fields are not used. A decay and a frequency shift, observed in these microwave experiments, are the quantities which describe the high-lossy materials very indirectly. Two basic strategic questions are thus posed: (a) What is the physical meaning of the constitutive parameters characterizing electromagnetic processes in high lossy materials? (b) How can these parameters be precisely measured?
The use of a small ferrite-disk scatterer with internal magneto-dipolar-mode (MDM) resonances in the channel of microwave propagation changes the transmission dramatically. Recently, it was shown that mesoscopic quasi-2D ferrite disks, distinguishing by multi-resonance MDM oscillations, demonstrate unique properties of artificial atomic structures: energy eigenstates, eigen power-flow vortices and eigen helicity parameters [17-23]. These oscillations can be observed as the frequency-domain spectrum at a constant bias magnetic field or as the magnetic-field-domain spectrum at a constant frequency. For electromagnetic waves irradiating a quasi-2D MDM disk, this small ferrite sample appears as a topological defect with time symmetry breaking. Long radiative lifetimes of MDMs combine strong subwavelength confinement of electromagnetic energy with a narrow spectral line width and may carry the signature of Fano resonances [22-26]. Interaction of the MDM ferrite particle with its environment has a deep analogy with the Fano-resonance interference observed in natural and artificial atomic structures [27].
MDM oscillations in a quasi-2D ferrite disk are macroscopically quantized states. Long range dipole-dipole correlation in position of electron spins in a ferromagnetic sample can be treated in terms of collective excitations of the system as a whole. If the sample is sufficiently small so that the dephasing length Lph of the magnetic dipole-dipole interaction exceeds the sample size, this interaction is non-local on the scale of Lph. This is a feature of mesoscopic ferrite samples, i.e., samples with linear dimensions smaller then Lph but still much larger than the exchange-interaction scales. MDMs in a quasi-2D ferrite disk possess unique physical properties. Being the energy-eigenstate oscillations, they also are characterized by topologically distinct structures of the fields. There are the rotating field configurations with power-flow vortices. At the MDM resonances, one observes power-flow whirlpools in the vicinity of a ferrite disk. For an incident EM wave, such a vortex topological singularity acts as a trap, providing strong subwavelength confinement and symmetry breakings of the microwave field [17-23, 28, 29].
For a MDM ferrite particle placed inside a microwave cavity with sufficiently low quality factor Q, one can observe the Fano-interference effects in microwave scattering. The spectrum of the MDM oscillations in a ferrite-disk particle is very rich [30, 31]. It contains different types of modes: the radial, azimuthal, and thickness modes [18]. Herein only the case of interaction of the cavity oscillation with the main mode in the MDM-spectrum sequence is considered.
In a widely used microwave cavity technique to determine the complex permittivity material parameters, the perturbation approach is commonly applied, which is characterized with limitation on permittivity and losses values as well as sample dimensions. The perturbation theory requires that sample permittivity, losses values and dimensions should be small enough so that the field distribution inside the empty cavity changes slightly when the cavity is loaded. Only with this limitation, the perturbation technique permits linkage via a simple formula between changes in the resonant frequency and loaded factor determined by the sample.
An example of such a formula, is [33]:
                                                        Δ              ⁢                                                          ⁢              f                                      f              0                                +                                    1              2                        ⁢            ⅈ            ⁢                                                  ⁢            Δ            ⁢                                                  ⁢                          1              Q                                      =                  k          ⁢                                          ⁢                                    -                              χ                e                                                    (                              1                +                                                      F                    sh                                    ⁢                                      χ                    e                                                              )                                                          (        3        )            where χe=χe′−iχe″ is the complex dielectric susceptibility, f0 is the frequency of an unloaded cavity, Δf and
  Δ  ⁢          ⁢      1    Q  are, respectively, the frequency and quality-factor shifts due to dielectric loading, Fsh is the constant dependent on the sample shape, and k is a calibration constant. It can be seen that both the frequency shift and the quality-factor shift depend on both the real and imaginary parts of the dielectric susceptibility. Separate experimental evaluation of these two kinds of shifts is possible only for small material losses. For high-lossy materials, the cavity resonance curve becomes so wide that evaluation of the quality-factor shift cannot presume exact evaluation of the frequency shift. Moreover, since the cavity resonance curve is wide, other resonances (originated, for example, from the terminal connectors) become prominent and an accurate detection of the resonant frequency shift appears to be very difficult.
This and the fact that in known standard microwave experiments, high-lossy material characteristics not only cannot be measured accurately, but also cannot be interpreted physically corrected (assuming that there are the real and imaginary parts of the permittivity and permeability parameters), there arises a need for realization of novel and appropriate microwave techniques for measuring properties of high-lossy materials. Initial studies of such a novel technique are shown in Ref. [34].
It is a purpose of the present invention to provide a method for microwave spectroscopy characterization of lossy materials including biological liquids.
Further purposes and advantages of this invention will appear as the description proceeds.